If X has a uniform density with α = 0 and β = 1, show that the random variable Y = –2 ∙ lnX has a gamma distribution. What are its parameters?
Answer to relevant QuestionsIf X has a uniform density with α = 0 and β = 1, show that Y = X– 1/ a with a> 0 has the Pareto distribution of Exercise 6.21 on page 184. With reference to Exercise 7.22, find In exercise If the joint probability distribution of X1 and X2 is given by f(x1, x2) = x1x2 / 36 (a) The joint distribution of Y1 = X1 + X2 and Y2 = X1 – X2; (b) The marginal ...Consider two random variables X and Y with the joint probability density Find the probability density of Z = XY2 by using Theorem 7.1 (as modified on page 216) to determine the joint probability density of Y and Z and then ...On page 215 we indicated that the method of transformation based on Theorem 7.1 can be generalized so that it applies also to random variables that are functions of two or more random variables. So far we have used this ...In Exercise 3.101 on page 108, the price of a certain commodity (in dollars) and its total sales (in 10,000 units) were denoted by P and S. Use the joint density given in that exercise and the distribution function technique ...
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